In general, the circuits for converting DC voltage to AC voltage--commonly referred to as inverters--are devices which can output a sinusoidal voltage with varying amplitude and frequency. Their operation is based on controlled switching of a DC voltage input using controlled electronic switches.
In a widely used class of inverters, the switching is performed so as to control the width of the output pulses, and it is for this reason that such devices are called PWM (Pulse Width Modulation) inverters. In these devices, in order to provide a sinusoidal output voltage at a given frequency, a sinusoidal reference signal having a desired frequency is compared with a triangular waveform. A rectangular wave voltage is obtained from the comparison which is utilized to control the inverter switches. Thus, a waveform is eventually output which consists of successive pulses at the same frequency as the reference signal and whose amplitude is equal to, or twice as great as, the value of the input DC voltage, depending on the structure of the set of switches and the control pattern thereof. This waveform, once suitably filtered, results in a sinusoidal voltage having the same frequency as the reference signal and an amplitude which is dependent on the input DC voltage.
The above-described operation scheme is based, of course, on an open-loop type of control, and is, therefore, unsuited to inverters which are to supply systems wherein the load may affect the output quantities of the inverter to any significant extent. In such cases, in fact, load variations may cause unacceptable alteration of the sinusoidal output waveform.
To obviate this drawback, a closed-loop control scheme has been proposed which operates in the so-called sliding mode. See, for instance, an article "Power conditioning system using sliding mode control" by M. Carpira, M. Marchesoni, M. Oberti and L. Puglisi, PESC '88 RECORD, April 1988.
According to that scheme, the output current and voltage from the inverter are respectively compared with a sinusoidal reference current and a sinusoidal reference voltage, and the result of the comparison, namely the error signal, is used to automatically determine the most appropriate switching sequence of the inverter switches to keep the output quantities at desired values.
The control principle of that technique can be described, in analytical terms by making reference to FIG. 1 of the accompanying drawing, which shows a diagram of a basic circuit structure comprising an inverter INV, being input a DC voltage U, a filter R, L, C, and a load Z. Normally, a transformer would be connected between the inverter output and the load which may be left out, however, of a first approximation to the circuit analysis. The equations that tie together the electric quantities in the circuit and, therefore, define the system to be controlled are the following: EQU u=Ri.sub.t +L(di.sub.t /dt)+v.sub.c EQU i.sub.t =i.sub.l +i.sub.c EQU i.sub.c =C(dv.sub.c /dt)
where:
u=output voltage of the inverter (or the transformer where provided); PA1 R=resistance of the filter; PA1 L=inductance of the filter; PA1 C=capacitance of the filter: PA1 i.sub.c =current through the capacitor: PA1 v.sub.c =voltage across the capacitor; PA1 i.sub.t =current through the leg R, L; PA1 i.sub.l =current through the load.
Assume that the voltage v.sub.c across the capacitor and its derivative dv.sub.c /dt are state variables, take the system state vector as x=[v.sub.c,dv.sub.c /dt].sup.T, and assume that the voltage v.sub.c is the quantity requiring control. Notice that the derivative of the voltage across the capacitor is readily obtained from a measurement of the capacitor charge current.
The aim is to have the output quantity of the inverter-filter system, i.e. the voltage v.sub.c across the capacitor, trace as closely as possible a predetermined reference quantity (reference voltage v.sub.r). This is obtained by causing the system state to follow a reference model represented by the sought voltage across the capacitor and by its derivative. Accordingly, the reference vector will be: EQU x.sub.r =[v.sub.r, dv.sub.r /dt].sup.T
and the state error: EQU x.sub.e =x.sub.r -x=[(v.sub.r -v.sub.c),(dv.sub.r /dt-dv.sub.c /dt)].sup.T
Additionally, a switching law will be defined, e.g. a weighted mean of the state errors: EQU s(x.sub.e)=K.sub.1 (v.sub.r -v.sub.c)+K.sub.2 (dv.sub.r /dt-dv.sub.c /dt).
The control quantity, that is the inverter output voltage u, is dependent on the switching law just defined, according to the following relations: EQU u=U.sub.max for s(x.sub.e)&gt;0 EQU u=U.sub.min for s(x.sub.e)&lt;0
where, U.sub.max and U.sub.min are the maximum and minimum values of the input voltage U, namely +U and 0 if U is a single-pole DC voltage.
Of special importance becomes, therefore, the relation: EQU s(x.sub.e)=0
In the state space, this equation can be represented by a straight line (switching line). If the control quantity u switches between U.sub.max and U.sub.min continuously, then the system is said to be operating in the sliding mode, i.e. the error x.sub.e will trace the switching straight line. From the above equation, there also must be: EQU d/dt[s(x.sub.e)]=0
By substituting the system equations in the latter and solving for the control quantity, the equivalent control quantity u.sub.eq is obtained. This is defined as the instant value of the quantity that should be input to the system to get the desired output.
The condition for the sliding mode to exist is expressed by the relation, EQU U.sub.max &lt;u.sub.eq &lt;U.sub.min
That is, the equivalent control quantity should never fall outside the limiting values of U.sub.max and U.sub.min. Should this occur, the system would evolve freely in the state space along paths dictated by the system own characteristics, until it crosses the straight line of existence of the sliding mode. Since x.sub.e represents the state error, the system operation point sought will correspond to the condition x.sub.e =0.
The control technique just expressed can provide systems with excellent dynamic response features and low sensitivity to changes in the construction parameters and to noise.
According to the foregoing theoretical discussion, in a sliding mode condition, the system would switch at infinite frequency. In pratice, however, the switching frequency would be a finite one, due to physical limitations of the inverter switches. Of course, the system would the closer approach ideal conditions, the higher is the switching frequency. To take said physical limitations into due account, a delay must be introduced in the system, such as by connecting a hysteresis comparator in the feedback loop which would set a tolerance range for the values of the control quantity.